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What does it mean for a set to be bounded?

  1. Oct 26, 2009 #1
    what does it mean for a set to be bounded??

    in the context of the hein-borel theorem

    i mean the mathematically rigorous definition
     
  2. jcsd
  3. Oct 27, 2009 #2

    Office_Shredder

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    Re: what does it mean for a set to be bounded??

    S a subset of Rn is bounded if there exists M>0 so that for all x in S, |x|<M
     
  4. Oct 27, 2009 #3
    Re: what does it mean for a set to be bounded??

    Another equivalent definition is that it has finite diameter, where

    [tex]\mathrm{diam}(S) = \sup_{x, y \in S}(\mathrm{dist}(x, y)).[/tex]

    This is applicable to any metric space (though the Heine-Borel theorem is not!).
     
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